Motivated by the work of Castro and Ozbagci [1]}, [2]}, we want to describe a method to paste two compatible \(\star \) -trisections along their boundaries.
The main technical observation that makes Theorem REF  work is that when we paste two standard pieces \(Z(C^0,C^1,C_{all})\)  along some connected components of \(C_0 \cup _{F_{all}} C_1\) , the resulting 4-manifold is also a standard piece whenever all the glued surfaces in \(F_{all}\)  have boundary.
The interested reader might note that our proof follows the same outline that the one of Theorem 2 of [1]} applied to the setting of \(\star \) -trisections.
